Context.Numerical simulations of planet-disk interactions are
usually performed with hydro-codes that – because they consider only
an annulus of the disk, over a 2D grid – cannot take into account
the global evolution of the disk. However, the global evolution governs
type II planetary migration, so that the accuracy of the planetary
evolution can be questioned.

Aims.To develop an algorithm that models the local planet-disk
interactions together with the global viscous evolution of the disk.

Methods.We surround the usual 2D grid with a 1D grid ranging over the real
extension of the disk. The 1D and 2D grids are coupled at their common
boundaries via ghost rings, paying particular attention to the fluxes
at the interface, especially the flux of angular momentum carried by
waves. The computation is done in the frame centered on the
center of mass to ensure angular momentum conservation.

Results.The global evolution of the disk and the local planet-disk
interactions are both well described and the feedback of one on the
other can be studied with this algorithm, for a negligible additional
computing cost with respect to the usual algorithms.

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